Data Collection Methods
Definition: Bias
On average, how “far away” is our estimate of the “truth”
- For example, is the sample mean gross weekly income in CS 1.1 close to the (unknown) population mean gross weekly income in the June quarter of 2011?
There can be multiple reasons for any biases in our estimates of the “truth”, for example:
- The way we calculated the estimate
- Our sample data is not representative of the population
- The way we measured the values
- …
Definition: Precision
On average, how variable is the estimate of the “truth”
- For example, consider a science experiment where you measure the velocity of a falling object
Like bias, there can be multiple reasons for imprecise estimates of the “truth”, for example:
- Not enough sample data
- The way we measured the values
- …
Definition: Simple random sample
All potential observations have the same chance to be selected for the sample
Why should we take random samples from the target population?
- Minimises potential biases due to selection
- Ensures that the selection of each observation is independent of another
# Randomly select ten integers (numbers) between 1 and 100,
# without replacement
sample(1:100, size = 10) [1] 100 10 5 89 42 12 2 69 51 87
Sampling error
The survey literature makes a distinction between sampling errors, which arise from the decision to take a sample rather than trying to survey the whole population (which is what a census tries to do)
— Wild & Seber (2000)
Sometimes—by chance—we can select a “bad” simple random sample that may not be representative of the population
# Randomly select ten integers (numbers) between 1 and 100,
# without replacement
sample(1:100, size = 10) [1] 6 9 1 7 3 5 4 10 2 8\[ (1/100)^{10} = 1 \times 10^{-20} \]
Definition: Stratified sample
All potential observations are first split into distinct groups (strata). Then we take a simple random sample of all potential observations within each group (stratum)
Why are stratified samples useful?
- The sampling strategy ensures that each stratum has “similar” observations
- Ensures that the selection of one observation is independent of another within and between stratum
# Randomly select ten integers (numbers) between 1 and 10,
# with replacement
sample(1:10, size = 10, replace = TRUE) [1] 10 2 2 6 9 1 1 10 3 4
Extensions to T011: Side-by-side plots by region
bwplot(region ~ income, data = nzis.df, pch = "|",
xlab = "Gross Weekly Income ($)", ylab = "Region",
main = "NZer's gross weekly income snapshot in 2011 by region")
The variable is plotted side-by-side for each level of the categorical variable. The goal of side-by-side plots is to compare and contrast the plotted variable between levels
With the lattice R package, we can make side-by-side plots of:
- Dot plots,
stripplot() - Box plots,
bwplot() - Bar plots,
barchart()(and with colour)
Extensions to T011: Panel plots by qualification
histogram( ~ income | qualification, data = nzis.df, nint = 25,
xlab = "Gross Weekly Income ($)",
main = "NZer's gross weekly income snapshot in 2011 by qualification")
The variable is plotted for each level of the categorical variable in its own panel. The goal of panel plots is to also compare and contrast the plotted variable between levels
With the lattice R package, we can make panel plots of:
- Dot plots,
stripplot() - Box plots,
bwplot() - Histograms,
histogram() - Scatter plots,
xyplot() - Bar plots,
bachart()
Extensions to T011: Introducing colour by sex
stripplot( ~ income, group = sex, data = nzis.df, jitter.data = TRUE,
factor = 10, xlab = "Gross Weekly Income ($)",
main = "NZer's gross weekly income snapshot in 2011 by sex",
auto.key = list(title = "Sex", space = "right"))
The variable is plotted and the values are colour-coded by the levels of the categorical variable. The goal of colour is to help distinguish between levels
With the lattice R package, we can make use of colour in:
- Dot plots,
stripplot() - Scatter plots,
xyplot() - Bar plots,
bachart()(and with side-by-side bars)
CS 2.1: Exploring pass.time
stripplot( ~ pass.time, data = lightspeed.df, jitter.data = TRUE,
factor = 5, main = "Measurements of passage time for light from Newcomb's experiment",
xlab = "Passage time (millionths of a second)")
Recall that the theoretical passage time for Newcomb’s experiment was 24.8296 millionths of a second.
CS 2.2: Exploring GillRate versus Calcium
bwplot(GillRate ~ Calcium, data = respiration.df, pch = "|",
factor = 5, main = "Respiration rate versus the tank's calcium level",
xlab = "Calcium level", ylab = "Respiration rate (gbpm)")
Recall that we want to judge if the observed differences in the experimental data are due to a “signal” rather than “noise”
CS 2.3: Exploring LungCap by Smoke
histogram( ~ LungCap | Smoke, data = lung.df,
main = "Lung capacity by Smoker status", nint = 10,
xlab = "Lung capacity (unitless)")
Remember the goal of side-by-side plots is to compare and contrast
CS 2.3: Exploring LungCap vs. Age by Smoke
xyplot(LungCap ~ Age | Smoke, data = lung.df,
main = "Lung capacity versus Age by Smoker status",
xlab = "Age (years)", ylab = "Lung capacity (unitless)")
Remember the goal of side-by-side plots is to compare and contrast
CS 2.3: Exploring LungCap vs. Age by Smoke & Sex
xyplot(LungCap ~ Age | Smoke + Sex, data = lung.df,
main = "Lung capacity versus Age by Smoker status and Sex",
xlab = "Age (years)", ylab = "Lung capacity (unitless)")
Remember the goal of side-by-side plots is to compare and contrast